Application of data-driven and physics-driven models in predicting vibratory responses of nonlinear dynamic systems

Abstract

The investigation of chaotic vibrations is essential for understanding the vibro-responses of engineering structures subjected to external excitations. This understanding is crucial for developing advanced strategies to control chaotic structural instability and sensitivity. Traditional methods for investigating chaotic vibration behavior rely on physics-based model establishment, where physical models are mathematically analyzed through complex calculations of differential equations. Although the development of analytical and numerical theories is relatively mature, the costly human labor required for feature engineering and high demands for expert knowledge in mathematical and physical domains limit its application in engineering fields to a certain extent. Therefore, this research aims to establish an innovative approach for predicting the chaotic responses of nonlinear models in the engineering field by proposing data-driven models to accomplish supervised learning regression tasks. The application of these proposed data-driven models in predicting chaotic responses of various nonlinear system models is conducted in a completely data-driven and non-intrusive manner. This thesis implements prediction tasks for chaotic vibrations of different types of nonlinear dynamic systems based on both physics-driven and data-driven models. These nonlinear systems serve as fundamental reference models and are widely applied in various engineering fields. Specifically, the physics-based investigations in this work focus on comparing the advantages of the developed P-T method over the 4th-order Runge-Kutta method in terms of accuracy and reliability. Additionally, studies on chaotic vibration prediction based on data-driven models are also carried out in this thesis. Three hybrid neural networks are proposed, and their architectures are thoroughly explained. The effectiveness and robustness of these models are sequentially enhanced. Specifically, their ability to handle chaotic sequences has evolved from considering temporal correlations to considering spatiotemporal correlations, and their capability to manage the length of inputs and outputs has progressed from fixed to variable. Besides the inherent advantages of data-driven investigation compared to physics-driven methods, the superior performance of the proposed data-driven models over conventional benchmarks in terms of training time and testing loss is quantitatively demonstrated. The continuous development of measuring equipment has facilitated easier access to substantial high-quality data. Thus, the findings of this research provide new insights into the investigation of chaotic responses and are valuable for analyzing and understanding chaotic vibrations with greater efficiency. The optimized results obtained in this research are expected to offer practically sound guidance for optimizing engineering structural design and enhancing performance when considering chaotic or nonlinear vibrations.